Monday Analysis Seminar: Potential theoretic proof of Hsu’s result on removable singularities of the heat equation

2013-7-22 14:45 - 2013-7-22 16:15
Faculty of Science Buliding #3 Room 210
Kentaro Hirata (Hiroshima University)
In 2010, Hsu gave a necessary and sufficient condition for solutions of the heat equation on $(\Omega\setminus\{0\})\times(0,T)$ to be extended to $\Omega\times(0,T)$. His proof is based on the integral representation and several estimates of the Green function
on a circular cylinder. In the same year, Hui gave another proof using the parabolic Schauder estimate and the maximum principle. In this talk, we will give a simple proof using well known results obtained by Watson (1976).